An H-matrix accelerated direct solver employing the high-order Chebyshev-based Boundary Integral Equation (CBIE) method has been formulated, tested, and profiled for performance on high contrast dielectric materials and electrically large perfect electric conductor objects. The matrix fill performance of the CBIE proves to be fast for small to moderately sized problems compared to its counterparts, e.g. the locally corrected Nystr\"om (LCN) method, due to the way it handles the singularities by means of a global change of variable method. However, in the case of electrically large scattering problems, the matrix fill and factorization still dominate the solution time when using a direct solution approach. To address this issue, an H-Matrix framework is employed, effectively resolving the challenge and establishing the CBIE as a competitive high-order method for solving scattering problems with poorly conditioned matrix equations. The efficacy of this approach is demonstrated through numerical results.

翻译：本文提出、测试并分析了采用高阶Chebyshev边界积分方程法的H-矩阵加速直接求解器，针对高对比度电介质材料和电大尺寸理想导体目标的性能表现进行了评估。与同类方法（如局部修正Nyström方法）相比，CBIE通过全局变量变换处理奇异性，在小到中等规模问题上展现出更快的矩阵填充性能。然而，对于电大尺寸散射问题，采用直接求解方法时，矩阵填充与分解仍主导求解时间。为解决此问题，本文引入H-矩阵框架，有效克服了这一挑战，使CBIE成为求解病态矩阵方程散射问题的具有竞争力的高阶方法。数值结果验证了该方法的有效性。